6 Following are intrest rates annual percentage rates for a

6. Following are intrest rates (annual percentage rates) for a 30-year-fixed-rate mortgage from a sample of lenders in a certain city. It is reasonable to assume that the population is approximately normal. 4.327, 4.461, 4.547, 4.585, 4.365, 4.774, 4.842. Find the upper bound of the 99% confidence interval for the mean rate. Round your answer three decimal places.

Solution

Sample Mean = 4.4823 SD = 0.1859 Sample Size (n) = 7 Standard Error (SE) = SD/root(n) = 0.0703 alpha (a) = 1-0.99 = 0.01 t(a/2, n-1 ) = 3.7074 Margin of Error (ME) = t(a/2,n-1)x SE = 0.2606 99% confidence interval is given by: Sample Mean +/- (Margin of Error) 4.4823 +/- 0.2606 = (4.222 , 4.743)